A conventional car reading lamp shown in FIG. 1 comprises a base 1, an upper cap 2 and a lamp plate. The upper cap 2 has a central opening 20, a projection 21 (22) respectively on two opposite side walls defining the central opening 2 to fit in a hole 30 (31) to enable the light plate 3 to swing up or down pivotally with the projections 21, 22 as pivots. So the angle of the lamp plate 3 can be changed. Then the base 1 and the upper cap 2 are combined tightly with screws. However, this conventional car reading light has no means to secure the lamp plate 3 at an angle when the lamp plate 3 rotates to the right or to the left, so the angle of the reading lamp is liable to change because of a bumping or a sudden stop when a car is running.